For the DWT approach, the basic functions to filter the initial topographic signal are obtained from a single prototype wavelet called the “Mother” wavelet “*ψ*(*x*)” by translation and dilation [40,41]. The mother wavelet is discretized using Eq. (1) where *m* and *n* are, respectively, the translation and dilation parameters. Then, the logarithmic scaling of both dilation and translation steps (*a*_{0} = 2 and *b*_{0} = 1) generates an orthogonal wavelet shown in Eq. (2). The DWT of the global topographic signal (called *f*(*x*)) is defined by Eq. (3) where $\psi \xafm,n(x)$ is the conjugate of the wavelet function. Finally, the reconstruction of the global topographic signal *f*(*x*) is given by Eq. (4)Display Formula

(1)$\psi m,n(x)=1a0m\psi (x\u2212nb0a0ma0m)$

Display Formula(2)$\psi m,n(x)=2\u2212m2\psi (2\u2212mx\u2212n)$

Display Formula(3)$W(m,n)=\u2329\psi \xafm,n(x),f(x)\u232a$

Display Formula(4)$f(x)=\u2211m,nW(m,n)\psi m,n(x)$